### Video Transcript

Which vector is equivalent to ๐ฎ plus ๐ฏ?

Looking at our figure, we see these two vectors making up the sides of a four-sided shape. Since the length of this side equals the magnitude of vector ๐ฏ and so does the length of this side, while these two sides of our shape have lengths equal to the magnitude of vector ๐ฎ, we know the shape overall is a parallelogram. Using this shape then, there are actually two ways to find our answer.

Starting at point ๐ด, we could follow along vector ๐ฎ and then after that vector ๐ฏ, and the tip of vector ๐ฏ points to where the sum of these two vectors lies. Here weโre using whatโs called the tip-to-tail method. Note that the tail of vector ๐ฏ lies at of the tip of vector ๐ฎ. Arranged this way, the sum of these two vectors ๐ฎ plus ๐ฏ is indicated by a vector that goes from the tail of the first vector, vector ๐ฎ, to the tip of the second vector, vector ๐ฏ.

We mentioned that thereโs a second way to solve for ๐ฎ plus ๐ฏ. And our shape now shows us how. ๐ฎ plus ๐ฏ is equivalent to ๐ฏ plus ๐ฎ. So we could get the same result by starting at the tail of vector ๐ฏ and then where its tip meets the tail of vector ๐ฎ, following that vector to its end. This approach gives us the same result of vector ๐ฎ plus vector ๐ฏ. In terms of the corners of our parallelogram, we see that this resultant vector joins point ๐ด to point ๐ท. We can express a vector from point ๐ด to point ๐ท like this. This, then, is our final answer. Vector ๐ฎ plus vector ๐ฏ equals vector ๐๐.